Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×#121 | C2 |
| hypercenter | #121 | D29 |
| hypocenter | C29 | #532 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90807 | C2 | semidirect |
| 2. C29×#121 | C2 | semidirect |
| 3. #11745302 | C2 | semidirect |
| 4. #11745301 | C2 | semidirect |
| 5. D4×Dic29 | C2 | semidirect |
| 6. #11745292 | C2 | semidirect |
| 7. C2×C4×Dic29 | C2 | semidirect |
| 8. #11745255 | C2 | semidirect |
| 9. #11745250 | C2 | semidirect |
| 10. #11745247 | C2 | semidirect |
| 11. #11745243 | C2 | semidirect |
| 50. C2×Dic29 | D4 | semidirect |
| 71. C4×C29 | #41 | semidirect |
| 76. Dic29 | #41 | semidirect |
| 90. #121 | D29 | semidirect |
| 95. C29 | #532 | semidirect |
| 160. C4 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90807 | 2 |
| C29×#121 | 2 |
| #11745302 | 2 |
| #11745301 | 2 |
| D4×Dic29 | 2 |
| #11745292 | 2 |
| C2×C4×Dic29 | 2 |
| #11745255 | 2 |
| #11745250 | 2 |
| #11745247 | 2 |
| #11745243 | 2 |
| #532 | 29 |